2023/11/26 by Christophe Charlier, Charlier, Christophe · 5 citations
Economics, Econometrics and Finance · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2311.15285
openalex publication_date 2023/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study hole probabilities of two-dimensional Coulomb gases with a general potential and arbitrary temperature. The hole region U is assumed to satisfy ∂ U⊂ S, where S is the support of the equilibrium measure μ. Let n be the number of points. As n → ∞, we prove that the probability that no points lie in U behaves like exp(-Cn2+o(n2)). We determine C in terms of μ and the balayage measure ν= Bal(μ|U,∂ U). If U is unbounded, then C also involves the Green function of Ω with pole at ∞, where Ω is the unbounded component of U. We also provide several examples where ν and C admit explicit expressions: we consider several point processes, such as the elliptic Ginibre, Mittag-Leffler, and spherical point processes, and various hole regions, such as circular sectors, ellipses, rectangles, and the complement of an ellipse. This work generalizes previous results of Adhikari and Reddy in several directions.